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Abstract

We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse trigonometric functions. Understanding these cuts is essential for working with the single-valued counterparts, the common approach to encoding multi-valued functions in computer algebra systems. While the defining choices are usually simple (typically portions of either the real or imaginary axes) the cuts induced by the expression may be surprisingly complicated. We have made explicit and implemented techniques for calculating the cuts in the computer algebra programme Maple. We discuss the issues raised, classifying the different cuts produced. The techniques have been gathered in the BranchCuts package, along with tools for visualising the cuts. The package is included in Maple 17 as part of the FunctionAdvisor tool.

BranchCuts.pdf: The final publication is available at link.springer.com

Status

Published

ID Code

32511

Additional Information

The functionality described in the paper is built into Maple, version 17 and above, where it is used by default for queries to the FunctionAdvisor. The code provided here (in the .mpl file) offers users of earlier versions some of the functionality. It is designed for use in Maple 16 and may also work with those earlier versions which still contain the FunctionAdvisor. For information on working with the code see the Appendix of the paper, the help in Maple 17 and the introductory worksheet provided here (the .mw file).